In this paper we extend a conjecture of Ash and Sinnott relating niveau one Galois representations to the mod p cohomology of congruence subgroups of SLn(Z) to include Galois representations of… (More)

Let F̄p be an algebraic closure of a finite field of characteristic p. Let ρ be a continuous homomorphism from the absolute Galois group of Q to GL(3, F̄p) which is isomorphic to a direct sum of a… (More)

In two previous papers [AGM02,AGM08] we computed cohomology groups H(Γ0(N);C) for a range of levels N , where Γ0(N) is the congruence subgroup of SL4(Z) consisting of all matrices with bottom row… (More)

We give several resolutions of the Steinberg representation Stn for the general linear group over a principal ideal domain, in particular over Z. We compare them, and use these results to prove that… (More)

Abstract. We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a… (More)

For any arithmetic group, a set of geometrically-defined cohomology classes is constructed which spans the cohomology of the group with rational coefficients in the highest nonvanishing dimension… (More)

We prove the following theorem: Let F be an algebraic closure of a finite field of characteristic p. If ρ is a continuous homomorphism from the absolute Galois group of Q to GLn(F) which is… (More)

We consider statistical properties of the sequence of ordered pairs obtained by taking the sequence of prime numbers and reducing modulo m. Using an inclusion/exclusion argument and a cut-off of an… (More)

Ash's research was partially supported by NSF Grant DMS-8919696. Conjecturally, any “algebraic” automorphic representation on GL(n) should have an n-dimensional Galois representation attached. Many… (More)